This study presents the new algorithm Q-CODA for disaggregating precipitation data from daily to sub-daily values. The method leverages the relationship between daily precipitation totals and sub-daily maximum values, which is assumed and shown to be quasi-comonotonic, meaning that high daily precipitation totals are strongly associated with high sub-daily maximum values. The quasi-comonotonicity assumption is incorporated into the methodology via an upper bound copula. The algorithm is applied to 91 observational stations in Spain, and multiple other methodologies are included in the study as benchmarks.

A wide variety of evaluation metrics are applied, shedding light on which aspects of sub-daily precipitation the various methodologies handle well and which they struggle with (e.g., temporal consistency, the fraction of dry days, representation of extreme rainfall events).

The paper is generally well written and, as far as I can tell, methodologically sound. It appears that both Q-CODA and the benchmark methods are implemented according to best practices, which ensures a fair comparison. 

I recommend that the paper be accepted with minor revisions, but have some suggestions that could strengthen the existing analysis.

Specific Comments

Page 4, lines 120-121

There are some references missing from the list at the back. I found two, Lee et al. (2022) and Chodhury et al. (2025), but there may be more throughout the document. I recommend that the authors check all citations and ensure they are included in the reference list.

Page 4, lines 126-127

Could you please describe the quality control that was applied to the observational data? It doesn’t have to be a full and detailed account, but a brief mention of what type of homogeneity testing was applied or a reference to the dataset would be helpful.

Page 5-6, Section 3

The methodology could benefit from clearer presentation in certain sections. For example, on line 150-151, you write about “the upper bound copula C+, representing perfect positive dependence (comonotonicity)...” which is then presented in Equation (2). After the equation, you write: “This copula implies that X and Y increase together almost surely, which aligns with the quasi-comonotonic behaviour observed between daily precipitation totals and sub-daily maxima.” The transition from perfect dependence to quasi-comonotonic behaviour is not entirely clear. 

Additionally, while the benchmarks are described clearly, the description of the Q-CODA methodology is more difficult to follow, perhaps due to the level of detail. The flowchart certainly helps, and after reading Section 3 a couple of times it does make sense, but it could be more accessible. Could you add a simplified example showing how the comonotonic upper bound is translated into target maxima and used during the iterative adjustment process? This is key to understanding the method. 

Page 11, line 290

The parenthesis in the cited paper should be after the name when it is in running text, i.e., “The ELU activation function was chosen by Bhattacharyya et al. (2024)...” rather than “(Bhattacharyya et al. 2024)”.

This issue recurs later on lines 302, 303, and 344, but I may have missed other instances. While this is a minor formatting issue, I recommend that the authors carefully check all citations to ensure they follow the correct format.

General Comments

Evaluation Metrics

The evaluation metrics are described in the main text, but references or equations are not provided. While this makes the main text more readable, it would be useful to include an appendix with a fuller description of the metrics, including equations and references (e.g., for the Nash-Sutcliffe Efficiency and Wasserstein distance). This would improve the reproducibility of the study. I understand the code will also be made available, but it would still be good if the paper included all information needed to interpret and recreate the results. 

Assumption of Quasi-Comonotonicity

The assumption of quasi-comonotonicity underpins the methodology, and the authors argue that the heterogeneity of precipitation regimes in Spain makes the results broadly applicable. While this argument is pretty convincing, I can think of precipitation regimes where the quasi-comonotonicity assumption might not hold as well. For example:

• In regions like northwestern Europe or the Pacific Northwest of the US and Canada, storm tracks bring sustained moderate precipitation over long periods of time, which may weaken the relationship between daily totals and sub-daily maxima.
• In monsoon regions, short-lived, strong convective systems could contribute to very high sub-daily maxima without corresponding high daily totals. This could weaken or break the dependence between daily totals and sub-daily maxima.

Could the authors expand on the discussion of quasi-comonotonicity and the applicability of Q-CODA in other regions? This might fit best in the Discussion section.

How sensitive is Q-CODA to deviations from the quasi-comonotonicity assumption? For example, could the authors test the algorithm on artificial datasets where the correlation between daily totals and sub-daily maxima is systematically reduced? This would help determine how far the assumption can deviate before the method’s performance degrades.

Performance Variability Across Stations

The Q-CODA algorithm performs well across most evaluation metrics, but some outliers appear (in Figure 6b and 6f for example), suggesting that the method struggles a bit at certain stations. This is to be expected, but it would be interesting to investigate these cases further. For example:

• Do these outliers correspond to stations with lower correlation values in Figure 2, potentially indicating weaker quasi-comonotonic dependence?
• Are there locations where all methods perform poorly, potentially pointing to data quality issues or precipitation processes that are difficult to capture with disaggregation methods?

Computational Feasibility

The paper does not discuss the computational costs of Q-CODA relative to the benchmarks. Given the iterative nature of the algorithm, this could be an important consideration, particularly for larger datasets or real-time applications. Please add a discussion of the computational efficiency of Q-CODA as compared to the benchmark methods. Even better, you could perform a comparative test of the computational costs. I am thinking of runtime, where parallelization might be an option for some of these methods, but also computational costs and energy usage (which can be checked with tools like CodeCarbon in python).

The manuscript presents Q-CODA, a novel copula-based framework for temporal disaggregation of daily precipitation into hourly time scales. The primary methodological contribution lies in exploiting the quasi-comonotonic dependence between daily total and sub-daily maxima though the Frechet-Hoeffding upper bound copula, combined with KNN based seeding and an iterative adjustment scheme. The approach is supported by a comprehensive multi-metric validation framework that takes into account accuracy, distributional fidelity, structural realism and hydrological relevance.

The manuscript is well presented, methodologically sophisticated and addresses a significant hydrological problem. The key strength of the paper lies in the explicit use of quasi-comonotonicity as a structural constraint, which poses as an advancement over the prevalent temporal disaggregation procedures. The comparative evaluation against multiple temporal disaggregation models under a 5-fold cross-validation scheme enhances the robustness and credibility of the results. The benchmark disaggregation methodologies have been implemented carefully and appear to be applied in a technically sound manner. The inclusion of precipitation dataset from 91 meteorological stations lying across diverse climatic regimes of Spain is commendable. The evaluation framework appropriately considers both upper-tail behaviour and key statistical and temporal properties of the hourly series, thereby ensuring that model performance is assessed rigorously.

Overall, the manuscript appears to have the potential to make an impactful contribution to the field of stochastic rainfall disaggregation.

My primary concerns largely overlap with those raised by Referee #1, specifically with respect to 1) the robustness and general applicability of the quasi-comonotonicity assumption 2) the need for improved clarity in the explanation of the proposed methodological framework 3) inclusion of a more detailed description of the evaluation metrics employed in the present study 4) the issue of missing references

Based on the author’s response, in my assessment, these four concerns appear to have been adequately addressed. Therefore, I recommend acceptance of the manuscript, provided that the revisions described are fully reflected in the final version of the manuscript.

General comments:

The authors provide a new algorithm for disaggregation daily into hourly precipitation with special focus on preserving sub-daily maxima. The main innovation is to use a Fréchet–Hoeffding upper bound copula to condition sub-daily maximum precipitation values on daily totals. The method outperforms four well selected benchmark methods i.e. a nearest-neighbour resampling method, a Poisson cluster-based rainfall generator, a multiplicative random cascades and a deep learning technique. The manuscript is short, well written to the point concise avoiding unnecessary text burden. The presented approach is novel and shows excellent performance. I have only a few comments for improvement of the manuscript. Publication is recommended after minor revisions.

Comments for improvement:

1. Section 3.3: Please provide some more information about the implementation of the k-nn method, e.g. how is a neighbour sampled (equation) and how many neighbours are considered (equation).
2. Section 4.4: This refinement of the hourly precipitation pattern in the 3^rd step of the algorithm is quite empirical and may contradict the model concepts of step 1 and 2. Please comment.
3. Lines 320ff: The discussion of the NRSP is not relevant here, since it is not a disaggregation approach but a continuous simulation model. This section could be shortened or removed.
4. The model is mainly non-parametric or relying on empirical probability distributions. This makes its regionalisation i.e. the application for unobserved locations almost impossible. This limitation should be discussed in the conclusions.
5. The missing spatial component does currently not allow mesoscale hydrological applications. This should also be discussed as limitation more in detail in the conclusions.

“Capturing the Extremes: A Quasi-Comonotonicity-Based Algorithm for Disaggregating Daily to Hourly Rainfall” is an interesting and novel study, which I recommend for publication after revisions to the manuscript.

Please see my feedback and comments below:

a) The abstract should include quantifiable values of the main results.

b) Figure 5 – Remove P^max_1h from subplot titleand rescale (h).  Recommended to add median boxplots.

c) Figure 7 – Subplot titles should include only “T = XX years.”

d) Include a Q–Q plot comparing simulated and observed rainfall datasets for both daily hourly maxima and full hourly scales for selected stations. Selection could be based on elevation or regional grouping.

e)  It would be much better if the author(s) could add a separate section for the discussion.

More Comments:

1. L115 – How consistent is the data on a yearly basis? Although a station may have >90% overall data availability, some years could still have significant missing data.
2. General – Inconsistent use of “section” and “sect.”
3. L91–95 – Remove or move to another section. The same applies to L96–104 and L120–125.
4. 158 – Specify which previous methods are being referred to.
5. L206 – Why was a 5-fold used? Also, divide the sentence for clarity.
6. L243 – Explain why 0.04 mm was selected.
7. L293 – Check the use of the word “by.”
8. L331 – Rewrite this sentence for clarity.
9. 342 – Use the full form of MELODIST in the previous sentence.
10. L375 – Clarify whether this analysis was done for each station individually or for all stations together.
11. L408, L416 – Explain how these are benchmark methods; if not justified, consider removing the term.
12. L413–415 – Rewrite to avoid redundancy with the figure reference. Check the term “daily maximum”- it appears to refer to a daily maximum 1-hour value.
13. L417 – Replace with “high-temporal-resolution.”
14. L446, L473 – The use of “robust” needs more justification.
15. L450–453, L465 – Rewrite these lines as suggested above for clarity and conciseness.